We consider a financial market with liquidity cost as in Çetin, Jarrow and Protter [3] where the supply function S(s, ν) depends on a parameter ε ≥ 0 with S(s, ν) = s corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi [6] of the super-hedging cost of an option written on such a stock, we provide a Taylor expansion of the super-hedging cost in...

In this work, we derive an analytical solution for the value of Parisian up-and-in calls by using the “moving window” technique developed by Zhu and Chen [15] for pricing European-style Parisian up-and-out calls. Our pricing formula can be applied to both European-style and American-style Parisian up-and-in calls, due to the fact that with an “in” barrier, the option holder cannot do or decide ...

Stock loans are collateral loans with stocks used as the collateral. This paper is concerned with a stock loan valuation problem in which the underlying stock price is modeled as an exponential phase-type Lévy model. The valuation problem is formulated as the optimal stopping problem of a perpetual American option with a time-varying exercise price. When a transformation is applied to the perpe...

This paper assesses the empirical performance of an intertemporal option pricing model with latent variables which generalizes the Black-Scholes and the stochastic volatility formulas. We derive a closed-form formula for an equilibrium model with recursive preferences where the fundamentals follow a Markov switching process. In a simulation experiment based on the model, we show that option pri...

NIKUNJ KAPADIA is with the Isenberg School of Management at the University of Massachusetts. T he recent proliferation of hedge funds has brought to the forefront the types of trading strategies that distinguish hedge funds from the more conservative mutual funds. Two major sets of trading strategies have been in the spotlight: market-neutral trades, and trades that rely on the spread between t...

In practice, all option strategies are decided in advance, given the investor’s belief of the stock price. In this paper, instead of deciding in advance the most appropriate hedging option strategy, an LP problem is formulated, by considering all significant Greek parameters of the Black-Scholes formula, such as delta, gamma, theta, rho and kappa. The optimal strategy to select will be simply d...

We analyze how the presence of financial markets affects optimal exercise real options for a risk averse agent. Extending results Shackleton and Sodal (2005), we characterize rule in terms benchmark portfolio, even case an incomplete market, facilitating minimal martingale measure. unambiguously effect idiosyncratic on speed option. further show that systematic can accelerate execution reduce v...

Within the framework proposed by Mussa and Rosen (1978) for modelling quality differentiation, we allow consumers to buy simultaneously different variants of the same indivisible good. We call this the ”joint purchase option”. We show that this option dramatically affects price competition: while a unique equilibrium always prevails when consumers are assumed to make mutually exclusive purchase...

To provide one motivation for the development of ARCH models (next handout), we briefly discuss here some difficulties associated with the Black Scholes formula, which is widely used to calculate the price of an option. For example, consider a European call option for a stock. This is the right to buy a specific number of shares of a specific stock on a specific date in the future, at a specifi...

In this paper we consider the valuation of an option with time to expiration T and pay-oo function g which is a convex function (as is a European call option), and constant interest rate r, in the case where the underlying model for stock prices (S t) is a purely discontinuous process (hence typically the model is incomplete). The main result is that, for \most" such models, the range of the va...